Beispiel Nr: 04
$ \text{Gegeben:} ax^{2}+bx+c=0 \\ \text{Gesucht:} \\ \text{Lösung der Gleichung} \\ \\ ax^{2}+bx+c=0 \\ \textbf{Gegeben:} \\ \frac{1}{4}x^2-2 =0 \\ \\ \textbf{Rechnung:} \\ \begin{array}{l|l|l|l} \begin{array}{l} \text{Umformen}\\ \hline \frac{1}{4}x^2-2 =0 \qquad /+2 \\ \frac{1}{4}x^2= 2 \qquad /:\frac{1}{4} \\ x^2=\displaystyle\frac{2}{\frac{1}{4}} \\ x=\pm\sqrt{8} \\ x_1=2,83 \qquad x_2=-2,83 \end{array}& \begin{array}{l} \text{a-b-c Formel}\\ \hline \\ \frac{1}{4}x^{2}+0x-2 =0 \\ x_{1/2}=\displaystyle\frac{-0 \pm\sqrt{0^{2}-4\cdot \frac{1}{4} \cdot \left(-2\right)}}{2\cdot\frac{1}{4}} \\ x_{1/2}=\displaystyle \frac{-0 \pm\sqrt{2}}{\frac{1}{2}} \\ x_{1/2}=\displaystyle \frac{0 \pm1,41}{\frac{1}{2}} \\ x_{1}=\displaystyle \frac{0 +1,41}{\frac{1}{2}} \qquad x_{2}=\displaystyle \frac{0 -1,41}{\frac{1}{2}} \\ x_{1}=2,83 \qquad x_{2}=-2,83 \end{array}& \begin{array}{l} \text{p-q Formel}\\ \hline \\ \frac{1}{4}x^{2}+0x-2 =0 \qquad /:\frac{1}{4} \\ x^{2}+0x-8 =0 \\ x_{1/2}=\displaystyle -\frac{0}{2}\pm\sqrt{\left(\frac{0}{2}\right)^2- \left(-8\right)} \\ x_{1/2}=\displaystyle 0\pm\sqrt{8} \\ x_{1/2}=\displaystyle 0\pm2,83 \\ x_{1}=2,83 \qquad x_{2}=-2,83 \end{array}\\ \end{array}$